By far the best Kat build is DFG first. It has longer range than Shunpo, so when you are going in on someone you just roll through your keys (You do smartcast everything on Kat right?) and they die. That first kill is a billion times more important than anything else you can possibly do on Kat. That reset is so absurdly critical.
DFG means you can kill an opponent with a mobility skill before they can get away. This lets you 1v1 duel people much more effectively. It also lets you teamfight waaaay better, because in team fights you have to deal with shields and heals and stacking CC, so the faster someone dies the better. Really, Kat is all about that first reset. Get a kill, then either Zhonyas if the entire enemy teams looks like they are going to pile in on you or Shunpo into their backfield and hope that their squishies were damaged enough by your ult that you can kill them with a simple eqw burst. Assuming they were hurt enough to die to that, you now pentakill them. If not, you killed one target with DFG combo and chunked someone else. And that is the goal of an assassin.
The best Kat's I've seen rush Sorc Shoes and DFG. From there it is situational. Deathcap and Zhonyas are both amazing, Void Staff and Abyssal are both strong depending on what you are against. Other niche items are good in their niches.
There are two newb trap items on Kat: Liandry's and Gunblade.
-Haunting Guise isn't a bad buy, but a poke centric item that deals its damage slowly over time is awful on an assassin that absolutely MUST instakill a target. Not to mention Kat doesn't even have a single skill that synergizes at all with the item. Look at the champions that buy it, they have either extreme range poke or some innate synergy.
-Gunblade has the problem of wasted stats and a bad build path. Lifesteal isn't going to help Kat. AD is mediocre and doesn't scale with Deathcap. The slow active is actually pretty useful. But when do you buy it? Most Kat's try to rush it, but holy crap is Kat weak with just a Hextech Revolver. Her skills are AoE so they don't heal for much, and why would you even want to invest in sustain on a roam-assassin based on instakilling people?
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though i hardly ever use DFG because i totally forget that it's there. Q.Q)
. If you are against AD I usually go Seeker's then DFG.
or 
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instead of
because ive found that, for ME, 
because flash is so important if your E is down. :/ so many decisions....
